The defeat means Tottenham have cut Chelsea's lead at the top of the table to just four points with six games remaining, and after the match Conte warned his players that they will need to match the intensity and determination of their London rivals if they are to secure the title.
United's performance was one of their best since Mourinho took charge last summer and the Portuguese praised his players' attitude.
But Chelsea does have a more favourable run-in than Tottenham.
"If someone thinks it's normal for Chelsea to win the title I think this season is not normal, because we started the season as underdogs".
"They deserved to win because they showed more desire than us, more motivation", said the Italian, whose side face Tottenham in the FA Cup semi-finals next weekend.
"We need a little more quality and different qualities in some positions to make the squad stronger, but in terms of character and the human side I have one of the best groups ever", said the former Real Madrid and Inter Milan manager. "In this case the fault is of the coach".
So, the Blues could drop points at The Hawthorns too, but I think they will absolutely wipe the floor with the teams they play in their four home games.
Conte's team looked as if they were running away with the Premier League title but have lost two of their last four games, also beaten at home by Crystal Palace earlier this month.
Mauricio Pochettino could perhaps be confident of a Champions League berth, but the title once again looked just beyond the edge of his team's grasp. "These three points were phenomenal".
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Jose Mourinho's squad avenged its 1-4 humiliation at Chelsea's Stamford Bridge in the first half of the season and the 0-1 FA Cup quarter-finals defeat against Antonio Conte's Blues. If they do, they will end their season on a 13 game winning streak. Rashford excelled up front, stretching Chelsea's center backs with the kind of movement and pace that Ibrahimovic would not be able to offer.
Looking confident and full of verve, United pushed forward with intent while Chelsea were unusually ineffective going forward, with Herrera doing an excellent marking job on Hazard.
On Sunday, United benefited from the tenacity of their defenders and Marcos Rojo's ability to answer Diego Costa's theatricality with his own version.
As good a tactical masterclass as it was from Mourinho, there was a touch of fortune about both goals.
In the build-up to the goal, Cahill was touch-tight with Jesse Lingard as Ashley Young's whipped cross aimed to pick out his teammate.
Conte insisted the pressure would not get to him.
Fans in the Stretford End chanted Herrera's name as he frustrated Hazard time and again in the first half.
Hit play on the video at the top of the page to watch the highlights as manchester United beat Chelsea 2-0 at old Trafford.
United's unbeaten run in the league extended to 22 games, the longest in Europe's top five leagues.
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